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Uniqueness and stability of the recovery of an absorbing obstacle from a knowledge of its scattering resonances

Published online by Cambridge University Press:  11 July 2007

C. Labreuche
Affiliation:
Thomson–CSF/LCR, Domaine de Corbeville, 91404 Orsay Cedex, France

Abstract

In a previous paper, I investigated the use (for the inverse scattering problem) of the resonant frequencies and the associated eigen far-fields. I showed that the shape of a sound soft obstacle is uniquely determined by a knowledge of one resonant frequency and one associated eigen far-field. Inverse obstacle scattering problems are ill-posed in the sense that a small error in the measurement may imply a large error in the reconstruction. This is contrary to the idea of continuity. I proved that, by adding some a priori information, the reconstruction becomes continuous. More precisely, continuity holds if we assume that the obstacle lies a fixed and known compact set.

The goal of this paper is to extend these results to the case of absorbing obstacles.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

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